A309934 Primes p such that p+2, (p+1)||p and (p+1)||(p+2) are primes (where || denotes concatenation in base 10).

41, 101, 107, 179, 191, 269, 311, 419, 521, 659, 821, 881, 1229, 1481, 4241, 4787, 8819, 10331, 11549, 13691, 14549, 14561, 14867, 15731, 17909, 18521, 20549, 21647, 22619, 23669, 23831, 26261, 27737, 35837, 38921, 39041, 40127, 42017, 43961, 44531, 46439, 47711, 48119, 48821

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3)=107 is in the sequence because 107, 109, 108107 and 108109 are primes.

Maple

Res:= {}:
for d from 1 to 6 do
  P:= select(isprime, {seq(i, i=10^(d-1)+1..10^d, 2)});
  T:= P intersect map(`-`, P, 2);
  Res:= Res union select(p -> isprime((10^d+1)*p+10^d) and isprime((10^d+1)*p+10^d+2), T);
od:
sort(convert(Res, list));

Mathematica

cm[{a_, b_}]:=Module[{m=(a+b)/2, il}, il=IntegerLength[m]; AllTrue[m*10^il+{a, b}, PrimeQ]]; Select[ Partition[Prime[Range[5100]], 2, 1], #[[2]]-#[[1]]==2&&cm[#]&][[;; , 1]] (* Harvey P. Dale, Feb 17 2024 *)

Prog

(Magma) [p:p in PrimesUpTo(2200)|IsPrime(p+2) and IsPrime(Seqint(Intseq(p) cat Intseq(p+1))) and IsPrime(Seqint(Intseq(p+2) cat Intseq(p+1)))]; // Marius A. Burtea, Aug 23 2019
(PARI) isok(k) = isprime(k) && isprime(k+2) && isprime(eval(Str(k+1, k))) && isprime(eval(Str(k+1, k+2))); \\ Jinyuan Wang, Aug 26 2019

Crossrefs

Cf. A001359, A309935.

Sequence in context: A142658 A228573 A273363 * A126588 A142794 A225888

Adjacent sequences: A309931 A309932 A309933 * A309935 A309936 A309937

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, Aug 23 2019

Status

approved